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I assume this is okay since your HW doesn't require you to derive the expression:

For an uniformly wound solenoid having N turns and length l, that satisfies l>>r (radius of the windings), and assuming the core of the solenoid is filled with air, B is magnetic field, u0 is the permittivity of free space, @ is the magnetic flux, I is the current, A is the cross-sectional area:

For a closely spaced coil, the induced electromagnetic field (emf), according to Faraday's Law is related to the negative time rate of change of magnetic flux, which should be proportional to the source current in the circuit. The proportionality constant, L, is the inductance.

Induced emf=-Nd@/dt =-LdI/dt

-> L=N@/I

The magnetic field in a solenoid is: B=u0NI/l

-> @=BA=u0NAI/l

-> L=N@/I=u0N2AI/l

The right-hand rule tells you which direction the induced magnetic field will be pointing. If you point your thumb in the direction of the current then your fingers curve around in the direction of the induced magnetic field.